Long Cable Lengths and ICP Transducers

Long cables can act as low pass filters on data signals that come from ICP transducers. The longer the cable, the higher the chance that frequency content in the signal is reduced or eliminated.

The article contains:

Background on how the cable capacitance attenuates higher frequency content

How to use a nomograph to determine the frequency cutoff due to cable

Recommendations how to reduce frequency content attenuation due to cable length

Background

The voltage that can be transmitted along a cable varies with signal frequency. The frequency dependency is related to the capacitance, or ability to store electric charge, of the transducer and cable combination.

The capacitance of a combined cable and transducer system determines how quickly the electric charge can be built up and discharged. The behavior of the combined cable and transducer is similar to a series resistor-capacitor (RC) circuit, which acts a low pass filter to the signal data.

This maximum frequency that can be transmitted for a given ICP transducer and cable is shown in Equation 1.

Equation 1: Maximum frequency for a cable and ICP transducer

In practical terms, this is not usually a problem with lower frequency testing up to 10,000 Hz. However, for higher frequency signals, cables longer than 100 feet (30 meters), should be checked out.

How to Read a Cable Nomograph

Rather than use Equation 1, it is possible to use an equivalent nomograph (Figure 1) to determine the maximum frequency that a specific ICP transducer and cable can measure.

Total Cable Capacitance – Multiply the length of the cable times the capacitance per unit of length of the cable

Example 1

For a 100 foot cable with a 5 Volt ICP transducer supplied at 2 milliAmps, the maximum frequency of the signal is 10,000 Hertz:

V = 5 Volts = Peak output of ICP transducer

Ic = 2 milliAmps = Current supply to ICP transducer

Total Cable Capacitance = 3000 picoFarads, where:

Cable length = 100 feet

Cable Capacitance = 30 picoFarads/foot

Total = Cable length x Cable Capacitance

To determine the maximum frequency of 10,000 Hz as shown in Figure 2:

The V / Ic -1 term is calculated, and is a value of 5

The intersection of 5 with the 3000 picoFarad line is plotted

A line is drawn down from the intersection to the frequency axis

Figure 2: 10,000 Hz is at the intersection of 3000 pF and 5

Keep in mind that a safety factor needs to be applied. 10 kHz is the maximum frequency, but it might be attenuated (see frequency rolloff section). A safety factor of at least 2x should be used.

Example 2

To improve the frequency performance of example 1, the current supply is increased from 2 milliAmps to 9 milliAmps. For a 100 foot cable with a 5 Volt ICP transducer supplied at 9 milliAmps, the maximum frequency of the signal is 100,000 Hertz:

V = 5 Volts = Peak output of ICP transducer

Ic = 9 milliAmps = Current supply to ICP transducer

Total Cable Capacitance = 3000 picoFarads, where:

Cable length = 100 feet

Cable Capacitance = 30 picoFarads/foot

Total = Cable length x Cable Capacitance

To determine the maximum frequency of 10,000 Hz as shown in Figure 3:

The V / Ic -1 term is calculated, and is a value of 0.55

The intersection of 0.55 with the 3000 picoFarad line is plotted

A line is drawn down from the intersection to the frequency axis

Figure 3: 100,000 Hz is at the intersection of 3000 pF and 0.55

Increasing the current supply to the transducer increases the maximum frequency. While increasing the current helps, the downside is reduced battery life when performing field measurements with a portable data acquisition equipment.

Frequency Rolloff and Filter Effects

The capacitance effect on the signal is a gradual roll off as the maximum frequency is approached. At some point the signal starts to be attenuated as shown in Figure 4.

Figure 4: Attenuation factor as maximum frequency is approached

It is possible to correct, to some extent, for this rolloff. The attenuation profile can be measured, and the amplitude content of some of the signal can be corrected, by using a Frequency Dependent Calibration. A Frequency Dependent Calibration multiples the reduced amplitude by the inverse of the attenuation as shown in Figure 5.

Figure 5: Frequency Dependent Calibration of Long Cable

This can be applied to the signal while it is being measured. While this cannot restore the frequency content perfectly up to the maximum frequency, it can make the measured signal more representative of the actual phenomenon being measured.

Simcenter Testlab

To use a Frequency Dependent Calibration, in the Channel Setup worksheet, choose “Tools -> Channel Setup Visibility” from the main menu.

Select “Freq Cal on” from the source field names and press the “Add” button (Figure 6).

Figure 6: Choose “Freq Cal On” from the source fields and press “Add”

Then in the upper right hand of Calibration worksheet, select Frequency Dependent Calibration (Figure 7).